Direct back-propagation contol of unstable nonlinear and nonstationary systems: difficulties, strategies and results
The paper discusses a generalized design of employing a Back-Propagation (BP) neural network (NN) as an intelligent controller that requires no identifier, to control time-varying and nonlinear (NL) possibly unstable systems of unknown parameters, stable or unstable, for achieving self-adaptive model reference control (MRC) or target-tracking control (TTC). Certain theoretical difficulties are discussed and some questions are left unanswered. However, it is shown that certain inevitable assumptions must be made, due to the impossibility of incorporating and awaiting convergence of an identifier if stabilization of an unknown nonlinear unstable system is to be expected, and regardless of the status of global nonlinear controllability theory. Algorithm designs are given for the BP-based control of SISO unstable time-varying and nonlinear systems when no identifier is employed, as is a computed example. Still, the weight initialization problem remains unsolved, as it presently requires several trials.